Re: NDSolve::ndsz
- To: mathgroup at smc.vnet.net
- Subject: [mg123865] Re: NDSolve::ndsz
- From: "Kevin J. McCann" <Kevin.McCann at umbc.edu>
- Date: Sat, 24 Dec 2011 07:07:40 -0500 (EST)
- Delivered-to: l-mathgroup@mail-archive0.wolfram.com
- References: <jd1rdq$1rt$1@smc.vnet.net>
If you plot the resulting a[t] and phi[t] over the range -1.1 <=t
<=-0.009, you will see that the two solutions blow up, as a result V[t]
does as well. I assume that the DE is physically motivated. Is there
some reason it should blow up?
Kevin
On 12/23/2011 7:15 AM, Gausstein wrote:
> Greetings,
> I have a problem solving two coupled differential equations using
> NDSolve.
> The following message appears: "NDSolve::ndsz: At t ==
> -0.008080592178665635`,
> step size is effectively zero; singularity or stiff system suspected.
>>> "
>
> Can NDSolve actually solve these equations? or should I better try
> another program?
> I have tried everything!!!
> I just need to know if it is possible to solve this equations with
> Mathematica.
> The code used is the following:
> *********************************************************************************************************
> H0 = 1/5000000;
> m = 3/500000000;
> A = 1/10^2;
> V0 = 3 H0^2;
> V0a = V0 - 1/2 A m^2 (2^(2 - 18 (1 - (7 Sqrt[51])/50)) 5^(2 - 21 (1 -
> (7 Sqrt[51])/50)));
>
> ti = -(11/10);
> tf = -Exp[-10];
> V[t_] := V0 + 1/2 m^2 phi[t]^2 + UnitStep[t + 1] (-V0 + V0a + 1/2 A
> m^2 phi[t]^2)
>
> value1 = 2^(1 - 21/2 (1 - (7 Sqrt[51])/50)) 5^(1 - 12 (1 - (7
> Sqrt[51])/50)) 11^(3/2 (1 - (7 Sqrt[51])/50));
> value2 = -3 2^(1 - 21/2 (1 - (7 Sqrt[51])/50)) 5^(2 - 12 (1 - (7
> Sqrt[51])/50) ) 11^(3/2 (1 - (7 Sqrt[51])/50) -
> 1) (1 - (7 Sqrt[51])/50);
>
> temp = NDSolve[{
>
> Derivative[1][a][t]/a[t]^2 ==Sqrt[1/3 (1/2 (Derivative[1][phi][t]/
> a[t])^2 +V[t])],
> Derivative[2][phi][t] + 2 Derivative[1][a][t]/a[t] Derivative[1][phi]
> [t] + m^2 a[t]^2 phi[t] (1 + A UnitStep[t + 1]) == 0,
> a[ti] == -1/(H0 ti),
> phi[ti] == value1,
> phi'[ti] == value2},
> {a, phi}, {t, ti, tf}, MaxSteps -> \[Infinity], InterpolationOrder ->
> All]
> ***************************************************************************************************************
> I know it looks pretty messy, but once it is copied into the Notebook
> (and if
> it is converted into StandardForm) it gets clearer.
> I really need help!!!!!!!!!!!!!!!!!!
> Thanks a lot!!!
>